I have a code on integration closed form.I have got the answer in terms of hypergeometric function. please explain about the solution what it actually means in simple way.A short description about the solution..Please help me.Its very much needful

syms a x y clear 
f = y/(y + x^(a/2));
F = int(f, x, 1, inf); 
vpa(F, 5)
int(f, x, 'IgnoreSpecialCases', true)

Solution is:

ans =
 numeric::int(y/(y + x^(a/2)), x == 1..Inf)

ans = 
x*hypergeom([1, 2/a], [2/a + 1], -x^(a/2)/y)

Answer 1

[Walter Roberson]

It does not mean much, as you did not put in the integration limit when you told it to ignore special cases.

[Swapna Havalgi]

Actually I donot know what is happening inside the code I just want the solution equation for the problem with the limits between 1 to infinity.Can i get the equation with above limits? Problem is Integration of I=y/(y+x^(a/2))dx with 1 to infinity limits.Please provide any solution

[Walter Roberson]

My tests with a different package suggests that there is no closed form integral for that. However if you have restrictions on the range of y or a then possibly there is a special case.

[Swapna Havalgi]

If we restrict on the range of y and a then under this condition can you suggest the solution equation?

[Torsten]

If it helps:

For a being an even integer >= 4, explicit solutions should exist.

Best wishes

Torsten.